Regular subalgebras of complete Boolean algebras

Journal of Symbolic Logic 66 (2):792-800 (2001)
It is proved that the following conditions are equivalent: (a) there exists a complete, atomless, σ-centered Boolean algebra, which does not contain any regular, atomless, countable subalgebra, (b) there exists a nowhere dense ultrafilter on ω. Therefore, the existence of such algebras is undecidable in ZFC. In "forcing language" condition (a) says that there exists a non-trivial σ-centered forcing not adding Cohen reals
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DOI 10.2307/2695044
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Andreas Blass (1988). Selective Ultrafilters and Homogeneity. Annals of Pure and Applied Logic 38 (3):215-255.

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